   Chapter 17.2, Problem 14E

Chapter
Section
Textbook Problem

Write a trial solution for the method of undetermined coefficients. Do not determine the coefficients.14. y" + 4y = cos 4x + cos 2x

To determine

To write: The trail solution for the method of undetermined coefficients.

Explanation

Given data:

The differential equation is,

y+4y=cos4x+cos2x (1)

Consider the auxiliary equation is,

r2+4=0

Roots of the equation are,

r=0±(0)24(1)(4)2(1){r=b±b24ac2afortheequationofar2+br+c=0}=±4i2=±2i

Write the expression for the complementary solution for the complex roots,

yc(x)=eαx(c1cosβx+c2sinβx)

Substitute 0 for α and 2 for β ,

yc(x)=e0x(c1cos2x+c2sin2x)=c1cos2x+c2sin2x

Re-write equation (1) by neglecting the term cos2x ,

y+4y=cos4x

Write the particular solution yp1(x)

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